> About a month back, a fellow senior manager tried stop this pattern by
> encouraging Bradley to do more remote lunchtime-meet-and-greets with
> his team **(so Bradley's budgets are spent on something other than
> training team members)**...

Taking what you said at face value. 

Trying to intentionally sabotage the growth of your junior engineers, wasting their training budget, and wasting their time, with this corporate double-speak and "social" subterfuge was an absolute colossal mistake.

At best, that suggestion was passive aggressive, dishonest, and cowardly. And not only it was deeply insulting to their intelligence. But at worst, implementing that idea would have been like shooting your own company in the foot, as there is often a 10X differential between top engineers and bottom ones.

At this point, I would suggest that the company backpedals completely and fires the senior colleague who came up with this underhanded idea. Getting rid of such a person would probably go a long way towards improving moral. 

Then, the next step should to offer all those engineers golden handcuffs. In other words, you should increase their compensation to be competitive with the marketplace, but delay and stagger those extra payments over the space of four years. 

Have your HR person research this topic, as this is not my area of expertise.   

> All people leaving his team, during exit interviews, seem to be using
> some kind of script where they praise him, and cite salary and
> incompetence by Bradley's boss's boss as their reason for leaving.
> This has happened 8 times. It feels very much staged.

Yes, colleagues will speak with each other. That doesn't mean there is a script. It just means that they'll often gripe about the same complaints when they're together. 

That doesn't mean anything. And it's not like you can stop it either. You do not operate a prison. You can't police their social interactions outside of work (or even during work).